where \(\epsilon _i\)  is distributed according to a standard Gumbel distribution. See [1]} for the details regarding how to construct such a choice model. We note that the deterministic portion of the utility is negative so that maximizing the utility corresponds to joining a queue with a shorter length (neglecting the random component of the utility as some realizations of the utility could be larger despite having a larger queue length if the realization of the corresponding random component of the utility happens to be small enough).
